Expansions (Including Substitution) - ICSE STD 9 MATHEMATICS Questions

Simplify using following identity :$(a \pm b)\left(a^2 \pm a b+b^2\right)=a^3 \pm b^3 \left(\frac{a}{3}-3 b\right)\left(\frac{a^2}{9}+a b+9 b^2\right)$

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Q 11[3 marks sum]3 Marks

If $a + b = 11$ and $a^2+ b^2= 65;$ find $a^3+ b^3.$

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Q 12[3 marks sum]3 Marks

Evaluate$:\frac{1.2 \times 1.2+1.2 \times 0.3+0.3 \times 0.3}{1.2 \times 1.2 \times 1.2-0.3 \times 0.3 \times 0.3}$

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Q 13[3 marks sum]3 Marks

Evaluate $:\frac{0.8 \times 0.8 \times 0.8+0.5 \times 0.5 \times 0.5}{0.8 \times 0.8-0.8 \times 0.5+0.5 \times .5}$

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Q 14[3 marks sum]3 Marks

Simplify : $( x + 6 )( x - 4 )( x - 2 )$

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Q 15[3 marks sum]3 Marks

Find : $(a - b)(a - b)(a - b)$

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Q 16[4 marks sum]4 Marks

Simplify :$\frac{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}{(x-y)^3+(y-z)^3+(z-x)^3}$

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Q 17[4 marks sum]4 Marks

The difference between two positive numbers is $4$ and the difference between their cubes is $316.$Find : The sum of their squares

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Q 18[4 marks sum]4 Marks

If $\frac{x^2+1}{x}=3 \frac{1}{3}$ and $\mathrm{x}>1 ;$ Find If $x^3-\frac{1}{x^3}$

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Q 19[4 marks sum]4 Marks

If $a^2+\frac{1}{a^2}=47$ and $a \neq 0$ find$:(i) a+\frac{1}{a},(ii)a^3+\frac{1}{a^3}$

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Q 20[4 marks sum]4 Marks

If $X \neq 0$ and $X+\frac{1}{X}=2$; then show that:$x^2+\frac{1}{x^2}=x^3+\frac{1}{x^3}=x^4+\frac{1}{x^4}$

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Q 21[5 marks sum]5 Marks

If $x=3+2 \sqrt{2 } $, find(i) $\frac{1}{x}$(ii) $x-\frac{1}{x}$(iii) $\left(x-\frac{1}{x}\right)^3$(iv) $x^3-\frac{1}{x^3}$

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Q 22[5 marks sum]5 Marks

If $x=\frac{1}{x-5}$ and $x \neq 5$. Find $: x^2-\frac{1}{x^2}$

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Q 23[5 marks sum]5 Marks

If $x^2+x^{\frac{1}{2}}=7$ and $x \neq 0$; find the value of:$7 x^3+8 x-\frac{7}{x^3}-\frac{8}{x}$

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Q 24[5 marks sum]5 Marks

If $2\left(x^2+1\right)=5 x$, find:$(i)x-\frac{1}{x}(ii)x^3-\frac{1}{x^3}$

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Q 25[5 marks sum]5 Marks

If $a - b = 4$ and $a + b = 6$; find $(i) a^2+ b^2(ii) ab$

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Expansions (Including Substitution) question types

Expansions (Including Substitution) questions

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Expansions (Including Substitution) MATHEMATICS - Expansions (Including Substitution)

Expansions (Including Substitution) question types

Expansions (Including Substitution) questions

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